stateswhich

Stateswhich is a term used in discussions of state-based systems to denote an operation or concept that selects states from a state space that satisfy a given predicate. In this sense, it functions as a filtering or selection mechanism applied to a set of states.

Formally, if S is a set of states and P is a predicate that can be evaluated on states, stateswhich(P) denotes the subset {s in S | P(s)}. This usage is analogous to filtering in programming or the selection operation in relational algebra. The concept can be applied to finite or infinite state spaces and is often used to reason about which states meet a particular condition within a model or specification.

In practical terms, stateswhich is commonly encountered in theoretical computer science topics such as automata theory, model checking, and graph query languages. For example, in model checking one might be interested in the set of reachable states that satisfy a temporal property P, effectively computing stateswhich(P) within the reachable portion of the state space. The operator can be combined with transitions, giving rise to filtered transition systems where only states meeting the predicate are considered for further exploration.

Status and terminology vary, as stateswhich is not a standardized formal operator in mainstream literature. It is often used as a descriptive label in theoretical discussions, drafts, or educational texts to describe the general idea of selecting states by a predicate. Variants of the concept may extend to multi-attribute state spaces and to predicates that depend on time, history, or other contextual factors.

See also: state space, predicate, filter, model checking, graph query languages, selection operator.